Mathematics A & B Revision Bundle

The transformation R of the plane is reflection in the line x = 0. (a) Write down the matrix M associated with R. [1] (b) Find M2 . [1] (c) Interpret the result of part (b) in terms of the transformation R. [1] 2 In this question you must show detailed reasoning. The equation x 2 - kx + 2k =...

Throughout all parts of this question, the resistance to the motion of a car has magnitude kv2 N, where vm s -1 isthe speed of the car and k is a constant. At first, the car travels along a straight horizontal road with constant speed 20m s -1 . The power developed by the car at this speed i...

Ryan has 6 one-pound coins and 4 two-pound coins. Ryan decides to select 3 of these coins at random to donate to a charity. The total value, in pounds, of these 3 coins is denoted by the random variable X. (a) Show that P(X = 3) = 1 . [2] The table below shows the probability distribution of X...

ig. 1.1 I A B K a The diagram in Fig. 1.1 represents a system of pipes through which a fluid can flow from two sources to three sinks. It also shows a cut a. The weights on the arcs show the capacities of the pipes in gallons per minute. (a) Add a supersource S and a supersink T to the netw...

The table shows some spreadsheet output. The values displayed in cells K21 and K22 are exact, but the values displayed in rows 21 and 22 in columns L, M and N have been found using appropriate cell formulae. ◢ K L M N 20 x e x 10x e x - 10x 21 0....30258E-09 22 1E-10 1 1 1.30258E-10 (a...

(a) The complex number a+ib is denoted by z. (i) Write down z*. [1] (ii) Find Re(iz). [2] (b) The complex number w is given by w = 5+i 3 . 2 -i 3 (i) In this question you must show detailed reasoning. Express w in the form x +iy . [2] (ii) Convert w to modulus-argument form. [2] 2 In this ...

A car of mass 800kg moves in a straight line along a horizontal road. There is a constant resistance to the motion of the car of magnitude 600 N. When the car is travelling at a speed of 15ms -1 the power developed by the car is 27 kW. Determine the acceleration of the car when it is travellin...

1 A website simulates the outcome of throwing four fair dice. Ten thousand people take part in a challenge using the website in which they have one attempt at getting four sixes in the four throws of the dice. The number of people who succeed in getting four sixes is denoted by the random variabl...

(a) State the dimensions of the following quantities. • Force • Velocity • Density [3] A student investigating the drag force F experienced by an object moving through air conjectures the formula 1 F = ku2^tm 2h3 , where • k is a dimensionless constant • u is the air velocity ...

A fair spinner has ten sectors, labelled 1, 2, …, 10. In order to start a game, Kofi has to obtain an 8, 9 or 10 on the spinner. (a) Find the probability that Kofi starts the game on the third spin. [2] (b) Find the probability that Kofi takes at least 5 spins to start the game. [1] (c) Determ...

Ten suitcases are to be transported in containers. Each container can hold a maximum of n kg, where n is a positive integer. The total weight of the ten suitcases is 216kg. You are given that at least 4 containers are needed to transport all ten suitcases. (a) Determine the maximum value of n fo...

You are given that (x1 , y1 ) = (0.9, 2.3) and (x2 , y2 ) = (1.1, 2.7). The values of x1 and x2 have been rounded to 1 decimal place. (a) Determine the range of possible values of x2 - x1 . [2] The values of y1 and y2 have been chopped to 1 decimal place. (b) Determine the range of pos...

A surface is defined in 3-D by z = 3x 3 + 6xy + y 2 . Determine the coordinates of any stationary points on the surface. [7] 2 A sequence is defined by the recurrence relation 4t n+1 -t n = 15n+17 for n H 1, with t 1 = 2. (a) Solve the recurrence relation to find the particular solution f...